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Computational Intelligence and Neuroscience
Volume 2017 (2017), Article ID 2747431, 10 pages
https://doi.org/10.1155/2017/2747431
Research Article

Ensembling Variable Selectors by Stability Selection for the Cox Model

1School of Science, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, China
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Correspondence should be addressed to Qing-Yan Yin

Received 13 May 2017; Revised 18 August 2017; Accepted 29 October 2017; Published 15 November 2017

Academic Editor: Paolo Gastaldo

Copyright © 2017 Qing-Yan Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. R. Cox, “Regression models and life-tables,” Journal of the Royal Statistical Society, vol. 34, no. 2, pp. 187–220, 1972. View at Google Scholar · View at MathSciNet
  2. J. Fan and R. Li, “Variable selection for Cox's proportional hazards model and frailty model,” The Annals of Statistics, vol. 30, no. 1, pp. 74–99, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. J. Q. Fan, Y. Feng, and Y. C. Wu, “High-dimensional variable selection for Cox’s proportional hazards model,” IMS Collections, vol. 6, pp. 70–86, 2010. View at Google Scholar
  4. D. R. Wang and Z. Z. Zhang, “Variable selection for linear regression models: a survey,” Journal of Applied Statistics and Management, vol. 29, no. 4, pp. 615–627, 2010. View at Google Scholar
  5. A. Miller, Subset Selection in Regression, Chapman and Hall/CRC Press, New Work, NY, USA, 2nd edition, 2002.
  6. R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society: Series B, vol. 58, no. 1, pp. 267–288, 1996. View at Google Scholar
  7. R. Tibshirani, “The lasso method for variable selection in the cox model,” Statistics in Medicine, vol. 16, no. 4, pp. 385–395, 1997. View at Publisher · View at Google Scholar · View at Scopus
  8. H. H. Zhang and W. Lu, “Adaptive Lasso for Cox's proportional hazards model,” Biometrika, vol. 94, no. 3, pp. 691–703, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Huang, S. Ma, and C.-H. Zhang, “Adaptive Lasso for sparse high-dimensional regression models,” Statistica Sinica, vol. 18, no. 4, pp. 1603–1618, 2008. View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Antoniadis, P. Fryzlewicz, and F. Letué, “The Dantzig Selector in Cox's Proportional Hazards Model,” Scandinavian Journal of Statistics, vol. 37, no. 4, pp. 531–552, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Du, S. Ma, and H. Liang, “Penalized variable selection procedure for Cox models with semiparametric relative risk,” The Annals of Statistics, vol. 38, no. 4, pp. 2092–2117, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. C. Liu, Y. Liang, X.-Z. Luan et al., “The L1/2 regularization method for variable selection in the Cox model,” Applied Soft Computing, vol. 14, pp. 498–503, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” Journal of the American Statistical Association, vol. 96, no. 456, pp. 1348–1360, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. Zou, “The adaptive lasso and its oracle properties,” Journal of the American Statistical Association, vol. 101, no. 476, pp. 1418–1429, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. L. Breiman, “Heuristics of instability and stabilization in model selection,” The Annals of Statistics, vol. 24, no. 6, pp. 2350–2383, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  16. L. I. Kuncheva, Combining Pattern Classifiers, Methods and Algorithms, John Wiley and Sons, New Jersey, NJ, USA, 2014.
  17. Z. H. Zhou, Machine Learning, Qinghua University Press, Beijing, China, 2016.
  18. M. Zhu and H. A. Chipman, “Darwinian evolution in parallel universes: a parallel genetic algorithm for variable selection,” Technometrics, vol. 48, no. 4, pp. 491–502, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. N. Meinshausen and P. Bühlmann, “Stability selection,” Journal of the Royal Statistical Society: Series B, vol. 72, no. 4, pp. 417–473, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  20. M. Zhu and G. Z. Fan, “Variable selection by ensembles for the Cox model,” Journal of Statistical Computation and Simulation, vol. 81, no. 12, pp. 1983–1992, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. S. J. Wang, B. Nan, S. Rosset et al., “Random Lasso,” The Annals of Applied Statistics, vol. 5, no. 1, pp. 468–485, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  22. L. Xin and M. Zhu, “Stochastic stepwise ensembles for variable selection,” Journal of Computational and Graphical Statistics, vol. 21, no. 2, pp. 275–294, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. B. Lin and Z. Pang, “Tilted correlation screening learning in high-dimensional data analysis,” Journal of Computational and Graphical Statistics, vol. 23, no. 2, pp. 478–496, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. B. Lin, Q. Wang, J. Zhang, and Z. Pang, “Stable prediction in high-dimensional linear models,” Statistics and Computing, vol. 27, no. 5, pp. 1401–1412, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. J. Che and Y. Yang, “Stochastic correlation coefficient ensembles for variable selection,” Journal of Applied Statistics, vol. 44, no. 10, pp. 1721–1742, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. C. Zhang, J. Zhang, and Q. Yin, “A ranking-based strategy to prune variable selection ensembles,” Knowledge-Based Systems, vol. 125, pp. 13–25, 2017. View at Publisher · View at Google Scholar
  27. B. Hofner, L. Boccuto, and M. Göker, “Controlling false discoveries in high-dimensional situations: boosting with stability selection,” BMC Bioinformatics, vol. 16, no. 1, article 144, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. A. Beinrucker, Ü. Dogan, and G. Blanchard, “Extensions of stability selection using subsamples of observations and covariates,” Statistics and Computing, vol. 26, no. 5, pp. 1059–1077, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  29. K. He, Y. Li, J. Zhu et al., “Component-wise gradient boosting and false discovery control in survival analysis with high-dimensional covariates,” Bioinformatics, vol. 32, no. 1, pp. 50–57, 2015. View at Publisher · View at Google Scholar · View at Scopus
  30. N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for Cox's proportional hazards model via coordinate descent,” Journal of Statistical Software , vol. 39, no. 5, pp. 1–13, 2011. View at Google Scholar · View at Scopus
  31. T. Therneau and P. Grambsch, Modeling Survival Data: Extending the Cox Model, Springer-Verlag, New York, NY, USA, 2000.
  32. C. L. Loprinzi, J. A. Laurie, H. S. Wieand et al., “Prospective evaluation of prognostic variables from patient-completed questionnaires,” Journal of Clinical Oncology, vol. 12, no. 3, pp. 601–607, 1994. View at Publisher · View at Google Scholar · View at Scopus
  33. N. Mantel, N. R. Bohidar, and J. L. Ciminera, “Mantel-Haenszel analyses of litter-matched time to response data, with modifications for recovery of interlitter information,” Cancer Research, vol. 37, no. 11, pp. 3863–3868, 1977. View at Google Scholar · View at Scopus
  34. A. Mkhadri and M. Ouhourane, “A group VISA algorithm for variable selection,” Statistical Methods and Applications, vol. 24, no. 1, pp. 41–60, 2015. View at Publisher · View at Google Scholar · View at Scopus
  35. H. Uno, T. Cai, M. J. Pencina, R. B. D'Agostino, and L. J. Wei, “On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data,” Statistics in Medicine, vol. 30, no. 10, pp. 1105–1117, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus